Discrete Painlev equations and random matrix averages

DOI10.1088/0951-7715/16/6/303zbMath1071.15026arXivmath-ph/0304020OpenAlexW2004139869MaRDI QIDQ4444052

Nicholas S. Witte, Peter J. Forrester

Publication date: 2003

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0304020

zbMATH Keywords

convergencediscrete Painlevé equationseigenvalue distributionsrandom matrix averages

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Discrete version of topics in analysis (39A12) Random matrices (algebraic aspects) (15B52) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Painlevé-type functions (33E17)

Related Items (12)

Asymptotic behaviours given by elliptic functions in ${\rm P_I}$ –${\rm P_V}$ ⋮ Moduli spaces of \(d\)-connections and difference Painlevé equations ⋮ Special polynomials associated with rational solutions of the Painlevé equations and applications to soliton equations ⋮ Painlevé transcendents and the Hankel determinants generated by a discontinuous Gaussian weight ⋮ The relationship between semiclassical Laguerre polynomials and the fourth Painlevé equation ⋮ On integrable Ermakov-Painlevé IV systems ⋮ Differential equations for deformed Laguerre polynomials ⋮ Nonperturbative theory of power spectrum in complex systems ⋮ Restoring discrete Painlevé equations from an E8(1)-associated one ⋮ τ-function of discrete isomonodromy transformations and probability ⋮ Applications in random matrix theory of a PIII′ τ-function sequence from Okamoto’s Hamiltonian formulation ⋮ Painlevé II in random matrix theory and related fields

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